And the Category Is.
And the Category Is.

Author: Ricky Tucker

Publisher: Beacon Press

Published: 2022-01-25

Total Pages: 250

ISBN-13: 0807003484

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A 2023 Lambda Literary Award Finalist in Nonfiction An Electric Literature “Most Anticipated LGBTQ+ Book of 2022” Selection A love letter to the legendary Black and Latinx LGBTQ underground subculture, uncovering its abundant legacy and influence in popular culture. What is Ballroom? Not a song, a documentary, a catchphrase, a TV show, or an individual pop star. It is an underground subculture founded over a century ago by LGBTQ African American and Latino men and women of Harlem. Arts-based and intersectional, it transcends identity, acting as a fearless response to the systemic marginalization of minority populations. Ricky Tucker pulls from his years as a close friend of the community to reveal the complex cultural makeup and ongoing relevance of house and Ballroom, a space where trans lives are respected and applauded, and queer youth are able to find family and acceptance. With each chapter framed as a “category” (Vogue, Realness, Body, et al.), And the Category Is . . . offers an impressionistic point of entry into this subculture, its deeply integrated history, and how it’s been appropriated for mainstream audiences. Each category features an exclusive interview with fierce LGBTQ/POC Ballroom members—Lee Soulja, Benjamin Ninja, Twiggy Pucci Garçon, and more—whose lives, work, and activism drive home that very category. At the height of public intrigue and awareness about Ballroom, thanks to TV shows like FX’s Pose, Tucker’s compelling narratives help us understand its relevance in pop culture, dance, public policy with regard to queer communities, and so much more. Welcome to the norm-defying realness of Ballroom.

Imagining Transgender
Imagining Transgender

Author: David Valentine

Publisher: Duke University Press

Published: 2007-08-30

Total Pages: 324

ISBN-13: 9780822338697

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DIVAn ethnography in which the author’s fieldwork with transgendered and transsexual individuals in New York City demonstrates the creation and confusion of gender identity labels./div

Basic Category Theory for Computer Scientists
Basic Category Theory for Computer Scientists

Author: Benjamin C. Pierce

Publisher: MIT Press

Published: 1991-08-07

Total Pages: 126

ISBN-13: 9780262660716

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Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Contents Tutorial • Applications • Further Reading

Triangulated Categories
Triangulated Categories

Author: Amnon Neeman

Publisher: Princeton University Press

Published: 2001-01-23

Total Pages: 468

ISBN-13: 9780691086866

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The first two chapters of this book offer a modern, self-contained exposition of the elementary theory of triangulated categories and their quotients. The simple, elegant presentation of these known results makes these chapters eminently suitable as a text for graduate students. The remainder of the book is devoted to new research, providing, among other material, some remarkable improvements on Brown's classical representability theorem. In addition, the author introduces a class of triangulated categories"--the "well generated triangulated categories"--and studies their properties. This exercise is particularly worthwhile in that many examples of triangulated categories are well generated, and the book proves several powerful theorems for this broad class. These chapters will interest researchers in the fields of algebra, algebraic geometry, homotopy theory, and mathematical physics.

An Invitation to Applied Category Theory
An Invitation to Applied Category Theory

Author: Brendan Fong

Publisher: Cambridge University Press

Published: 2019-07-18

Total Pages: 351

ISBN-13: 1108482295

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Category theory reveals commonalities between structures of all sorts. This book shows its potential in science, engineering, and beyond.

Non-hausdorff Completion, A: The Abelian Category Of C-complete Left Modules Over A Topological Ring
Non-hausdorff Completion, A: The Abelian Category Of C-complete Left Modules Over A Topological Ring

Author: Saul Lubkin

Publisher: World Scientific Publishing Company

Published: 2015-05-28

Total Pages: 352

ISBN-13: 9814667404

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This book introduces entirely new invariants never considered before, in homological algebra and commutative (and even non-commutative) algebra. The C-completion C(M), and higher C-completions, Cn(M), are defined for an arbitrary left module M over a topological ring A. Spectral sequences are defined that use these invariants. Given a left module over a topological ring A, under mild conditions the usual Hausdorff completion: M^ can be recovered from the C-completion C(M), by taking the quotient module by the closure of {0}.The new invariants and tools in this book are expected to be used in the study of p-adic cohomology in algebraic geometry; and also in the study of p-adic Banach spaces — by replacing the cumbersome 'complete tensor product' of p-adic Banach spaces, with the more sophisticated 'C-complete tensor product', discussed in this book.It is also not unlikely that the further study of these new invariants may well develop into a new branch of abstract mathematics - connected with commutative algebra, homological algebra, and algebraic topology.

Handbook of Categorical Algebra: Volume 1, Basic Category Theory
Handbook of Categorical Algebra: Volume 1, Basic Category Theory

Author: Francis Borceux

Publisher: Cambridge University Press

Published: 1994-08-26

Total Pages: 363

ISBN-13: 0521441781

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The Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence, with the first being essentially self-contained, and are accessible to graduate students with a good background in mathematics. In particular, Volume 1, which is devoted to general concepts, can be used for advanced undergraduate courses on category theory.

Hopf Algebras and Their Generalizations from a Category Theoretical Point of View
Hopf Algebras and Their Generalizations from a Category Theoretical Point of View

Author: Gabriella Böhm

Publisher: Springer

Published: 2018-11-01

Total Pages: 171

ISBN-13: 3319981374

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These lecture notes provide a self-contained introduction to a wide range of generalizations of Hopf algebras. Multiplication of their modules is described by replacing the category of vector spaces with more general monoidal categories, thereby extending the range of applications. Since Sweedler's work in the 1960s, Hopf algebras have earned a noble place in the garden of mathematical structures. Their use is well accepted in fundamental areas such as algebraic geometry, representation theory, algebraic topology, and combinatorics. Now, similar to having moved from groups to groupoids, it is becoming clear that generalizations of Hopf algebras must also be considered. This book offers a unified description of Hopf algebras and their generalizations from a category theoretical point of view. The author applies the theory of liftings to Eilenberg–Moore categories to translate the axioms of each considered variant of a bialgebra (or Hopf algebra) to a bimonad (or Hopf monad) structure on a suitable functor. Covered structures include bialgebroids over arbitrary algebras, in particular weak bialgebras, and bimonoids in duoidal categories, such as bialgebras over commutative rings, semi-Hopf group algebras, small categories, and categories enriched in coalgebras. Graduate students and researchers in algebra and category theory will find this book particularly useful. Including a wide range of illustrative examples, numerous exercises, and completely worked solutions, it is suitable for self-study.

Cohomology and Differential Forms
Cohomology and Differential Forms

Author: Izu Vaisman

Publisher: Courier Dover Publications

Published: 2016-08-17

Total Pages: 305

ISBN-13: 0486804836

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This monograph explores the cohomological theory of manifolds with various sheaves and its application to differential geometry. Based on lectures given by author Izu Vaisman at Romania's University of Iasi, the treatment is suitable for advanced undergraduates and graduate students of mathematics as well as mathematical researchers in differential geometry, global analysis, and topology. A self-contained development of cohomological theory constitutes the central part of the book. Topics include categories and functors, the Čech cohomology with coefficients in sheaves, the theory of fiber bundles, and differentiable, foliated, and complex analytic manifolds. The final chapter covers the theorems of de Rham and Dolbeault-Serre and examines the theorem of Allendoerfer and Eells, with applications of these theorems to characteristic classes and the general theory of harmonic forms.